In terms of the common currency, a couple of things. Yes, I had had it raised that a common currency may be less plausible in this situation than that of the euro, and I for a long time considered not including it in this. However, I had already mentioned it in previous bits of media and wanted to avoid confusing retcons whenever possible. Was it the right decision? Perhaps not, but currency and monetary policy is not something I'm an expert in or anything. I am aware that the Euro took a long time to adopt, and, while not shown on this timeline, I assumed the process was undertaken gradually roughly during the time between the exchange rate reforms and the final adoption, though yes this might not have been clearly put.
US domination is very much an issue, and a controversial one, in this world. There are a few counters though in-universe.
1. The Union is just good for peace and we don't want something like the Nazis to happen again, so we'll go along with it.
2. In Britain and Canada's case, there is a genuine increased fondness for America, in its role in protecting against a much scarier looking Nazi Germany, and the much longer term and later direct military alliance.
3. Europe has been thoroughly destroyed, even more so than in otl's WW2, even to the point of demographics in huge swathes of Europe being damaged for decades to come. Reconstruction will be a long and arduous process, and along the way and even afterwards Europe will be poorer than otl and struggling. For countries like Britain and Scandinavian countries, that weren't affected by the war but (certainly in Britain's case) have had huge economic difficulty, going along with America, losing some global independence, but gaining economic links across the Atlantic rather than with mainland Europe may well seem appealing, at least at first. However, as countries recover, resistance builds up, which leads to the 1981 crisis (and the subsequent reforms), and then to the period of little getting done in the 90s and 2000s because a lot of people are pretty against policies which they see as strengthening the American-dominated bloc.